The threat of global warming and the demand for reliable climate predictions pose a formidable challenge because the climate system is multiscale, high-dimensional and nonlinear. Spatiotemporal recurrences of the system hint to the presence of a low-dimensional manifold containing the high-dimensional climate trajectory that could make the problem more tractable. Here we argue that reproducing the geometrical and topological properties of the low-dimensional attractor should be a key target for models used in climate projections. In doing so, we propose a general data-driven framework to characterize the climate attractor and showcase it in the tropical Pacific Ocean using a reanalysis as observational proxy and two state-of-the-art models. The analysis spans four variables simultaneously over the periods 1979–2019 and 2060–2100. At each time $t$, the system can be uniquely described by a state space vector parametrized by $N$ variables and their spatial variability. The dynamics is confined on a manifold with dimension lower than the full state space that we characterize through manifold learning algorithms, both linear and nonlinear. Nonlinear algorithms describe the attractor through fewer components than linear ones by considering its curved geometry, allowing for visualizing the high-dimensional dynamics through low-dimensional projections. The local geometry and local stability of the high-dimensional, multivariable climate attractor are quantified through the local dimension and persistence metrics. Model biases that hamper climate predictability are identified and found to be similar in the multivariate attractor of the two models during the historical period while diverging under the warming scenario considered. Finally, the relationships between different subspaces (univariate fields), and therefore among climate variables, are evaluated. The proposed framework provides a comprehensive, physically based, test for assessing climate feedbacks and opens new avenues for improving their model representation.

中文翻译：

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在模型和观测中探索热带太平洋流形

全球变暖的威胁和对可靠气候预测的需求构成了巨大的挑战，因为气候系统是多尺度、高维和非线性的。系统的时空重现暗示存在一个包含高维气候轨迹的低维流形，这可能使问题更容易处理。在这里，我们认为再现低维吸引子的几何和拓扑特性应该是气候预测中使用的模型的关键目标。为此，我们提出了一个通用的数据驱动框架来表征气候吸引子，并使用再分析作为观测代理和两个最先进的模型在热带太平洋展示它。该分析同时涵盖 1979-2019 年和 2060-2100 年期间的四个变量。每次$吨$, 系统可以用一个参数化的状态空间向量来唯一描述$ñ$变量及其空间变异性。动力学被限制在维度低于我们通过流形学习算法（包括线性和非线性）表征的完整状态空间的流形上。非线性算法通过考虑其弯曲几何形状通过比线性更少的组件来描述吸引子，从而允许通过低维投影来可视化高维动力学。高维、多变量气候吸引子的局部几何和局部稳定性通过局部维度和持久性指标进行量化。识别并发现阻碍气候可预测性的模型偏差在历史时期两个模型的多元吸引子中相似，而在所考虑的变暖情景下存在分歧。最后，评估不同子空间（单变量场）之间以及气候变量之间的关系。提议的框架为评估气候反馈提供了一个全面的、基于物理的测试，并为改进其模型表示开辟了新途径。